Users may utilize product dispensers that dispense a variety of types of products such as, for example, sheet products, solids, liquids, gases, or products that include—or exhibit characteristics of—multiple phases of matter such as gels, aerosols, foams, and so forth. An automated product dispenser, for example, may be configured to dispense a quantity of a product in response to detection of the movement or presence of an object (e.g., a user's hand) by a sensor. As another example, an automated product dispenser may operate in “hang-mode” and may include a tear sensor that detects when a product, such as a sheet product, has been separated from a product roll and generates a signal that causes the dispenser to dispense additional sheet product of a predetermined length. Various settings for controlling the operation of a product dispenser may be configurable such as, for example, an incremental amount of the product dispensed during each dispensing cycle.